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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Psychol.</journal-id>
<journal-title>Frontiers in Psychology</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Psychol.</abbrev-journal-title>
<issn pub-type="epub">1664-1078</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="doi">10.3389/fpsyg.2025.1564880</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Psychology</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Parental/grandparental education involvement and adolescents&#x2019; learning engagement: a moderated mediation model</article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author" corresp="yes">
<name><surname>Xiang</surname> <given-names>Xiaoqing</given-names></name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
<xref ref-type="corresp" rid="c001"><sup>&#x002A;</sup></xref>
<uri xlink:href="https://loop.frontiersin.org/people/1905417/overview"/>
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<role content-type="https://credit.niso.org/contributor-roles/formal-analysis/"/>
</contrib>
<contrib contrib-type="author">
<name><surname>Huang</surname> <given-names>Xiaofeng</given-names></name>
<xref ref-type="aff" rid="aff1"><sup>1</sup></xref>
<uri xlink:href="https://loop.frontiersin.org/people/2990192/overview"/>
<role content-type="https://credit.niso.org/contributor-roles/writing-original-draft/"/>
<role content-type="https://credit.niso.org/contributor-roles/methodology/"/>
</contrib>
<contrib contrib-type="author">
<name><surname>Zhao</surname> <given-names>Mengyue</given-names></name>
<xref ref-type="aff" rid="aff2"><sup>2</sup></xref>
<role content-type="https://credit.niso.org/contributor-roles/data-curation/"/>
<role content-type="https://credit.niso.org/contributor-roles/writing-original-draft/"/>
</contrib>
<contrib contrib-type="author">
<name><surname>Wang</surname> <given-names>Jing</given-names></name>
<xref ref-type="aff" rid="aff3"><sup>3</sup></xref>
<role content-type="https://credit.niso.org/contributor-roles/writing-original-draft/"/>
</contrib>
<contrib contrib-type="author">
<name><surname>Shao</surname> <given-names>Qian</given-names></name>
<xref ref-type="aff" rid="aff4"><sup>4</sup></xref>
<uri xlink:href="https://loop.frontiersin.org/people/2955243/overview"/>
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<aff id="aff1"><sup>1</sup><institution>School of Psychology, Fujian Normal University</institution>, <addr-line>Fuzhou</addr-line>, <country>China</country></aff>
<aff id="aff2"><sup>2</sup><institution>Zhoukou Wentai Senior High School</institution>, <addr-line>Zhoukou</addr-line>, <country>China</country></aff>
<aff id="aff3"><sup>3</sup><institution>The Second Primary School of Cangwu Primary School Education Group</institution>, <addr-line>Lianyungang</addr-line>, <country>China</country></aff>
<aff id="aff4"><sup>4</sup><institution>College of Rehabilitation Science, Nanjing Normal University of Special Education</institution>, <addr-line>Nanjing</addr-line>, <country>China</country></aff>
<author-notes>
<fn fn-type="edited-by" id="fn0002">
<p>Edited by: Yael Fisher, Achva Academic College, Israel</p>
</fn>
<fn fn-type="edited-by" id="fn0003">
<p>Reviewed by: Francisco Manuel Morales Rodr&#x00ED;guez, University of Granada, Spain</p>
<p>Yuno Shimizu, Kokushikan University, Japan</p>
</fn>
<corresp id="c001">&#x002A;Correspondence: Xiaoqing Xiang, <email>xqxiang_edu@163.com</email></corresp>
</author-notes>
<pub-date pub-type="epub">
<day>07</day>
<month>08</month>
<year>2025</year>
</pub-date>
<pub-date pub-type="collection">
<year>2025</year>
</pub-date>
<volume>16</volume>
<elocation-id>1564880</elocation-id>
<history>
<date date-type="received">
<day>22</day>
<month>01</month>
<year>2025</year>
</date>
<date date-type="accepted">
<day>28</day>
<month>07</month>
<year>2025</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#x00A9; 2025 Xiang, Huang, Zhao, Wang and Shao.</copyright-statement>
<copyright-year>2025</copyright-year>
<copyright-holder>Xiang, Huang, Zhao, Wang and Shao</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</p>
</license>
</permissions>
<abstract>
<p>Parental and grandparental involvement are associated with students&#x2019; educational success. However, few studies have explored the different effects of parental and grandparent education involvement on students&#x2019; academic performance. This study constructed a hypothetical model of parental/grandparental education involvement and adolescents&#x2019; learning engagement, with personal growth initiative as the mediating variable and self-education expectation as the moderating variable, to investigate how parental/grandparental education involvement influences learning engagement. A total of 822 adolescents from middle schools in China participated in the study. The results revealed that parental/grandparental education involvement significantly and positively affected adolescents&#x2019; learning engagement. In the context of parental education involvement, the most important factor in promoting learning engagement is emotional leisure. In the context of grandparental education involvement, the most important factor in promoting learning engagement is academic support. Furthermore, personal growth initiative mediated the relationship of parental and grandparental education involvement, respectively. The relationship between parental/grandparental educational involvement and learning engagement was moderated by self-education expectation. However, the interaction effect between self-education expectation and education involvement (emotional leisure, teaching rules, academic support, life care) to predict learning engagement is different between parents and grandparents. For the situation where parents directly raise their children, the interaction term (emotional leisure/teaching rules/academic support &#x00D7; self-education expectation) significantly predicted learning engagement, indicating that self-education expectation moderated the direct effect of emotional leisure, teaching rules, academic support on learning engagement. For the situation where grandparents providing caregiving for grandchildren, only the interaction term emotional leisure &#x00D7; self-education expectation significantly predicted learning engagement, indicating that self-education expectation moderated the direct effect of emotional leisure on learning engagement. The objective of this study was to provide further empirical evidence regarding the discrepancies in the mechanisms by which parental/grandparental education involvement affects adolescents&#x2019; learning engagement, and to offer further insights into the promotion of learning engagement among adolescents.</p>
</abstract>
<kwd-group>
<kwd>grandparental education involvement</kwd>
<kwd>parental education involvement</kwd>
<kwd>personal growth initiative</kwd>
<kwd>learning engagement</kwd>
<kwd>moderated mediation model</kwd>
</kwd-group>
<counts>
<fig-count count="5"/>
<table-count count="10"/>
<equation-count count="0"/>
<ref-count count="55"/>
<page-count count="12"/>
<word-count count="8203"/>
</counts>
<custom-meta-wrap>
<custom-meta>
<meta-name>section-at-acceptance</meta-name>
<meta-value>Educational Psychology</meta-value>
</custom-meta>
</custom-meta-wrap>
</article-meta>
</front>
<body>
<sec sec-type="intro" id="sec1">
<label>1</label>
<title>Introduction</title>
<p>Learning engagement has gained considerable attention as a vital determinant of students&#x2019; academic performance, as it represents an active and fulfilling learning state characterized by vigor, commitment, and concentration (<xref ref-type="bibr" rid="ref3">Barber&#x00E1;-Tom&#x00E1;s et al., 2022</xref>). Positive engagement can reliably predict current academic success (<xref ref-type="bibr" rid="ref9003">Moreira et al., 2013</xref>) and influence various aspects of students&#x2019; future lives. Actively engaged middle-school students exhibit lower dropout rates and fewer problem behaviors, positioning them favorably for future careers (<xref ref-type="bibr" rid="ref2">Archambault et al., 2022</xref>). In China, parents highly emphasize their children&#x2019;s education, as academic achievement is crucial for prestigious university admission and well-compensated employment (<xref ref-type="bibr" rid="ref29">Moore, 2019</xref>). Academic success is considered the primary pathway to higher social status among junior-high-school students and is closely linked to future development (<xref ref-type="bibr" rid="ref19">Guo et al., 2018</xref>). Studies have also indicated a declining tendency in junior-high-school students&#x2019; learning engagement between their first and third years (<xref ref-type="bibr" rid="ref56">Zhou, 2021</xref>). Therefore, paying attention to this issue is of great importance for these students&#x2019; academic performance. Learning engagement is influenced by various factors, including individual characteristics, family dynamics, and school environment (<xref ref-type="bibr" rid="ref26">Li et al., 2023</xref>). Among these, parental education involvement (PEI) significantly determines secondary school students&#x2019; academic achievement (<xref ref-type="bibr" rid="ref51">Xiong et al., 2021</xref>).</p>
<p>With China&#x2019;s socioeconomic development, many young people are occupied with work, leaving them with insufficient time and energy to care for their children. This has led to the common phenomenon of grandparents raising children. The World Population Prospects of 2019 suggest that the number of Chinese older adults aged 65&#x202F;years or over will reach 366 million by 2050. Influenced by Confucianism, which emphasizes the collective family, many older adults in China shoulder extensive grandparenting responsibilities (<xref ref-type="bibr" rid="ref49">Wang et al., 2022</xref>), and over 50% of Chinese grandparents provide childcare to grandchildren (<xref ref-type="bibr" rid="ref23">Ko and Hank, 2014</xref>). Despite this prevalence, few studies have addressed the different effects of parental education involvement (defined as parent childcare, frequency of contact, provide financial support) and grandparental education involvement (defined as grandparent childcare, frequency of contact, the parents usually work in other places and provide financial support) on learning engagement. Moreover, research has shown discrepancies between parents and grandparents&#x2019; approaches to fostering children&#x2019;s personal growth initiative (PGI; <xref ref-type="bibr" rid="ref37">Sadruddin et al., 2019</xref>). Therefore, it is crucial to investigate, from the perspectives of parents and grandparents, the effects of educational involvement and PGI on learning engagement, as well as the underlying mechanisms involved.</p>
<sec id="sec2">
<label>1.1</label>
<title>PEI/GEI and learning engagement</title>
<p>PEI (parental education involvement) encompasses various behaviors that parents adopt to enhance students&#x2019; educational achievements based on diverse educational concepts and academic achievement expectations (<xref ref-type="bibr" rid="ref42">Seginer, 2006</xref>). The positive impact of PEI on middle-school students&#x2019; learning engagement has been consistently emphasized in research (<xref ref-type="bibr" rid="ref30">Chen et al., 2024</xref>). Active PEI correlates with enhanced academic outcomes, increased attendance rates, and overall student success. When parents engage in their children&#x2019;s schooling, students demonstrate higher academic achievement, school engagement, and motivation (<xref ref-type="bibr" rid="ref4">Barger et al., 2019</xref>). Studies among 9th and 10th graders in Jordan showed that PEI positively influenced students&#x2019; emotional engagement in school (<xref ref-type="bibr" rid="ref38">Sapungan and Sapungan, 2014</xref>). This implies that students with more involved parents are more likely to find school enjoyable, have high self-esteem, and perceive school as a satisfying experience. Thus, parental support and guidance play a crucial role in positively affecting students&#x2019; learning.</p>
<p>Few studies have directly explored the relationship between GEI (grandparental education involvement) and learning engagement. However, current research suggests that grandparental involvement has a positive impact on children&#x2019;s social skills and reduces the occurrence of internalizing and externalizing problem behaviors, which may subsequently influence adolescents&#x2019; learning engagement (<xref ref-type="bibr" rid="ref28">Luo et al., 2020</xref>). <xref ref-type="bibr" rid="ref52">Yorgason et al. (2011)</xref> investigated the association between grandparental involvement and positive outcomes for grandchildren. They found that, when grandparents are involved in their grandchildren&#x2019;s daily lives, the grandchildren exhibit greater sociability and increased learning engagement. Therefore, we propose the following hypothesis:</p>
<disp-quote>
<p><italic>H1:</italic> PEI and GEI are significant positive predictors of adolescent&#x2019;s learning engagement.</p>
</disp-quote>
</sec>
<sec id="sec3">
<label>1.2</label>
<title>PGI as a mediator</title>
<p>PGI encompasses cognitive and behavioral tendencies focused on active and intentional personal growth. This concept has been delineated into four relatively independent dimensions: readiness for change, planfulness, using resources, and intentional behaviors (<xref ref-type="bibr" rid="ref14">Dengyong et al., 2014</xref>). According to the theory of self-determination, individuals generally have three basic needs: autonomy, ability, and relationships (<xref ref-type="bibr" rid="ref12">Deci and Ryan, 2000</xref>). PGI is a manifestation of the need for autonomy as a vital intrinsic motivation that can significantly influence academic performance and emotional adaptation (<xref ref-type="bibr" rid="ref18">Grolnick and Slowiaczek, 1994</xref>). Researchers have suggested that positive academic performance is challenging unless students autonomously engage in learning (<xref ref-type="bibr" rid="ref41">Schnitzler et al., 2021</xref>). When students&#x2019; autonomous needs are met, they typically experience a sense of choice and self-recognition of their behavior (<xref ref-type="bibr" rid="ref13">Deci and Ryan, 2008</xref>; <xref ref-type="bibr" rid="ref16">Gagn&#x00E9; and Deci, 2005</xref>). Consequently, they become more willing to participate and invest in learning activities. Studies have indicated that fulfilling students&#x2019; autonomy needs enhances their internal motivation, leading to more positive learning engagement behaviors (<xref ref-type="bibr" rid="ref35">Reeve, 2012</xref>). Several studies have explored the relationship between PEI and students&#x2019; PGI, particularly among Chinese primary school students (<xref ref-type="bibr" rid="ref55">Zhao et al., 2021</xref>). The findings reveal that the manner and extent of PEI positively impact students&#x2019; autonomy. Parent&#x2019;s support and encouragement are crucial in cultivating students&#x2019; PGI, which closely correlates with their learning engagement (<xref ref-type="bibr" rid="ref26">Li et al., 2023</xref>). In summary, PEI and GEI are advantageous for students&#x2019; PGI, and PGI is linked to improved learning engagement. This suggests that PGI may mediate the relationship between PEI/GEI and learning engagement. Thus, we propose the following hypothesis:</p>
<disp-quote>
<p><italic>H2:</italic> PGI plays a mediating role in the link between PEI/GEI and learning engagement.</p>
</disp-quote>
</sec>
<sec id="sec4">
<label>1.3</label>
<title>Self-education expectation as a moderator</title>
<p>Apart from PGI, an individual&#x2019;s self-education expectation also modulates one&#x2019;s implementation of learning activities. Students&#x2019; educational expectations are closely related to their academic performance (<xref ref-type="bibr" rid="ref32">Pinquart and Ebeling, 2020</xref>). Students with higher self-education expectations work harder to learn to meet their expectations and achieve relatively better academic performance. One study proved that middle-school students&#x2019; self-education expectations has a positive impact on their academic development and can promote their degree of investment (<xref ref-type="bibr" rid="ref25">Li et al., 2020</xref>; <xref ref-type="bibr" rid="ref45">Shi et al., 2023</xref>). According to Bandura&#x2019;s triadic interactive determinism, behavior, cognition, and the environment are interconnected and interact during the social learning process (<xref ref-type="bibr" rid="ref8">Chai and Ye, 2024</xref>). Furthermore, the external environment influences individuals through inter-subjective factors. In this study, PEI and GEI were considered external environmental factors, while self-education expectation was considered an internal factor affecting individuals. Based on Bandura&#x2019;s ternary interaction theory, junior-high-school students&#x2019; learning engagement is influenced not only by PEI, GEI, and self-education expectation, but also by their combined effect (<xref ref-type="bibr" rid="ref40">Schmid and Garrels, 2021</xref>). Therefore, self-education expectation may act as a moderator in the pathway between PEI/GEI and learning engagement. Thus, we propose two hypotheses: self-education expectation significantly moderates the relationship between PEI and learning engagement (H3a), and self-education expectation significantly moderates the relationship between GEI and learning engagement (H3b).</p>
</sec>
<sec id="sec5">
<label>1.4</label>
<title>The present study</title>
<p>The present study examined the mediating and moderating factors in the association between PEI/GEI and learning engagement among adolescents in the Chinese context. It also explored the underlying mechanisms of this relationship by considering cognitive trait factors, including the mediating role of PGI and the moderating role of self-education expectation. By constructing two moderated mediation models (see <xref ref-type="fig" rid="fig1">Figure 1</xref>), this study contributes to the understanding of the mechanisms and differences underlying the influence of PEI and GEI on adolescents&#x2019; learning engagement. Additionally, it provides empirical support to guide adolescents&#x2019; learning engagement in a scientifically practical manner.</p>
<fig position="float" id="fig1">
<label>Figure 1</label>
<caption>
<p>Hypothetical model. The two models depict the relationships between the main variables. The arrows indicate the mechanism of influence between the variables. The independent variable in the left model is assumed to be parental education involvement, whereas that in the right model is grandparental education involvement.</p>
</caption>
<graphic xlink:href="fpsyg-16-1564880-g001.tif" mimetype="image" mime-subtype="tiff">
<alt-text content-type="machine-generated">Two diagrams show the relationships between educational involvement and other factors. The left diagram connects Parental Educational Involvement (PEI) with Learning Engagement (LE) and Self Education Expectation (SEE), influenced by Personal Growth Initiative (PGI) through hypotheses H1, H2, and H3(a). The right diagram is similar but involves Grandparental Educational Involvement (PEI), maintaining the same hypotheses labels: H1, H2, and H3(b).</alt-text>
</graphic>
</fig>
</sec>
</sec>
<sec sec-type="methods" id="sec6">
<label>2</label>
<title>Methods</title>
<sec id="sec7">
<label>2.1</label>
<title>Sample and data collection</title>
<p>This study was approved by the Ethics Committee for Scientific Research at the authors&#x2019; institution. Data were collected from 850 junior-high-school students using a paper-based questionnaire. After excluding invalid responses, 822 responses were retained, resulting in a response rate of 96.7%. Among these valid responses, 380 were from male students and 442 were from female students, with ages ranging from 12 to 15&#x202F;years (mean&#x202F;&#x00B1;&#x202F;standard deviation: 12.16&#x202F;&#x00B1;&#x202F;1.20). The participants were distributed across different grades, with 522 (63.5%) in Grade 1 of junior high school and 300 (36.4%) in Grade 2. Additionally, we categorized students based on their main caregivers, with 636 (77.4%) raised by parents and 186 (22.6%) raised by grandparents.</p>
</sec>
<sec id="sec8">
<label>2.2</label>
<title>Measurements</title>
<sec id="sec9">
<label>2.2.1</label>
<title>PEI/GEI</title>
<p>The study used the Parental/Grandparental Education Involvement Questionnaire (PIQ/GIQ), which was revised by <xref ref-type="bibr" rid="ref9004">Wu et al. (2018)</xref>. The original questionnaire comprised 22 items across four dimensions: emotional leisure (11 items), and teaching rules (3 items), academic support (4 items), life care (4 items). Responses were scored on a 5-point scale, ranging from 1 (never) to 5 (always). Examples items are &#x201C;Parents/Grandparents take care of your daily life,&#x201D; &#x201C;Parents/Grandparents exercise with me,&#x201D; &#x201C;Parents/Grandparents and I went on a trip,&#x201D; and &#x201C;Parents/Grandparents supervise my homework.&#x201D; The questionnaire demonstrated good reliability and validity. Cronbach&#x2019;s <italic>&#x03B1;</italic> coefficients of the PIQ in the present study were 0.73&#x2013;0.92, and those of the GIQ were 0.71&#x2013;0.89.</p>
</sec>
<sec id="sec10">
<label>2.2.2</label>
<title>Learning engagement</title>
<p>The Chinese version of the Utrecht Work Engagement Scale&#x2014;Student, developed by <xref ref-type="bibr" rid="ref39">Schaufeli et al. (2002)</xref> and revised by <xref ref-type="bibr" rid="ref9002">Fang et al. (2008)</xref>, was used to measure adolescents&#x2019; engagement in learning. The scale comprises 17 items across three dimensions: vigor (six items; e.g., &#x201C;I have much energy when I study&#x201D;), commitment (six items; e.g., &#x201C;I find studying valuable and meaningful&#x201D;), and concentration (five items; e.g., &#x201C;I am so concentrated that I forget everything when I study&#x201D;). Participants responded to the items on a 7-point Likert scale, with scores ranging from 1 (never) to 7 (always). Cronbach&#x2019;s alpha coefficient of the parent&#x2019;s questionnaire in the present study were 0.89&#x2013;0.90, and those of the grandparent&#x2019;s questionnaire were 0.85&#x2013;0.88.</p>
</sec>
<sec id="sec11">
<label>2.2.3</label>
<title>PGI</title>
<p>The Personal Growth Initiative Scale-II, developed by <xref ref-type="bibr" rid="ref36">Robitschek et al. (2012)</xref>, was used to assess PGI. This scale contains 16 items across four dimensions: ready for change (four items; e.g., &#x201C;I know what aspects of myself need to change&#x201D;), planning (four items; e.g., &#x201C;I know how to make a realistic plan to change myself&#x201D;), resource use (four items; e.g., &#x201C;I know how to make a realistic plan to change myself&#x201D;), and proactive behavior (four items; e.g. &#x201C;I can take advantage of any opportunity to grow&#x201D;). Items were scored on a 5-point scale ranging from 1 (strongly inconsistent) to 5 (strongly consistent). Cronbach&#x2019;s alpha coefficient of the parent&#x2019;s questionnaire in the present study were 0.78&#x2013;0.85, and those of the grandparent&#x2019;s questionnaire were 0.76&#x2013;0.80.</p>
</sec>
<sec id="sec12">
<label>2.2.4</label>
<title>Self-education expectation</title>
<p>Self-education expectation was measured by asking participants about the highest level of education they wished to attain in the future. The response options and assigned values were: secondary vocational and below&#x202F;=&#x202F;1, vocational college&#x202F;=&#x202F;2, university&#x202F;=&#x202F;3, and postgraduate and above&#x202F;=&#x202F;4. Scores ranged from 1 to 4, with a higher score indicating higher expectations.</p>
</sec>
</sec>
<sec id="sec13">
<label>2.3</label>
<title>Data analysis</title>
<p>First, we conducted descriptive statistics and correlation analyses using IBM SPSS 26.0. Subsequently, we tested the mediation and moderated mediation models using the IBM SPSS macro PROCESS (<xref ref-type="bibr" rid="ref20">Hayes, 2013</xref>), which has been widely used to test complex models, including mediated moderation and moderated mediation models. Models 4 and 5 in the PROCESS macro program<xref ref-type="fn" rid="fn0001"><sup>1</sup></xref> were used to analyze the mediating role of PGI and the moderating role of self-education expectation between PEI/GEI and learning engagement. Additionally, previous research has revealed that learning engagement differs based on grade and previous achievement (<xref ref-type="bibr" rid="ref31">Pi&#x00F1;eiro et al., 2019</xref>; <xref ref-type="bibr" rid="ref56">Zhou, 2021</xref>). Therefore, grade and previous achievement were included as control variables in this study.</p>
</sec>
</sec>
<sec sec-type="results" id="sec14">
<label>3</label>
<title>Results</title>
<sec id="sec15">
<label>3.1</label>
<title>Descriptive and correlation analysis</title>
<p>The results in <xref ref-type="table" rid="tab1">Tables 1</xref>, <xref ref-type="table" rid="tab2">2</xref> illustrate the means (M), standard deviations (SD), and correlation coefficients of all the variables. Not all forms of parental involvement are positively related to academic achievement (<xref ref-type="bibr" rid="ref7">Boonk et al., 2018</xref>). It is necessary to explore the different dimensions of parental/grandparental educational involvement. The four dimensions of PEI (<italic>r</italic> =&#x202F;0.113&#x2013;0.731, <italic>p</italic> &#x003C;&#x202F;0.01) and the four dimensions of GEI (<italic>r</italic> =&#x202F;0.146&#x2013;0.629, <italic>p</italic> &#x003C;&#x202F;0.05) demonstrated significant positive correlations with learning engagement, PGI, and self-education expectation.</p>
<table-wrap position="float" id="tab1">
<label>Table 1</label>
<caption>
<p>Descriptive statistics and bivariate correlations (parent).</p>
</caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th>Variable</th>
<th align="char" valign="top" char="&#x00D7;">
<italic>Min</italic>
</th>
<th align="char" valign="top" char="&#x00D7;">
<italic>Max</italic>
</th>
<th align="char" valign="top" char="&#x00D7;">
<italic>M</italic>
</th>
<th align="char" valign="top" char="&#x00D7;">
<italic>SD</italic>
</th>
<th align="char" valign="top" char="&#x00D7;">EL</th>
<th align="char" valign="top" char="&#x00D7;">TR</th>
<th align="char" valign="top" char="&#x00D7;">AS</th>
<th align="char" valign="top" char="&#x00D7;">LC</th>
<th align="char" valign="top" char="&#x00D7;">PGI</th>
<th align="char" valign="top" char="&#x00D7;">LE</th>
<th align="char" valign="top" char="&#x00D7;">SEE</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" valign="top">EL</td>
<td align="center" valign="top">1</td>
<td align="center" valign="top">5</td>
<td align="center" valign="top">3.020</td>
<td align="center" valign="top">0.893</td>
<td align="center" valign="top">1</td>
<td/>
<td/>
<td/>
<td/>
<td/>
<td/>
</tr>
<tr>
<td align="left" valign="top">TR</td>
<td align="center" valign="top">1</td>
<td align="center" valign="top">5</td>
<td align="center" valign="top">4.126</td>
<td align="center" valign="top">0.811</td>
<td align="center" valign="top">0.592<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">1</td>
<td/>
<td/>
<td/>
<td/>
<td/>
</tr>
<tr>
<td align="left" valign="top">AS</td>
<td align="center" valign="top">1</td>
<td align="center" valign="top">5</td>
<td align="center" valign="top">3.351</td>
<td align="center" valign="top">0.939</td>
<td align="center" valign="top">0.731<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.598<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">1</td>
<td/>
<td/>
<td/>
<td/>
</tr>
<tr>
<td align="left" valign="top">LC</td>
<td align="center" valign="top">1</td>
<td align="center" valign="top">5</td>
<td align="center" valign="top">4.076</td>
<td align="center" valign="top">0.814</td>
<td align="center" valign="top">0.543<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.567<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.553<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">1</td>
<td/>
<td/>
<td/>
</tr>
<tr>
<td align="left" valign="top">PGI</td>
<td align="center" valign="top">1</td>
<td align="center" valign="top">5</td>
<td align="center" valign="top">3.397</td>
<td align="center" valign="top">0.811</td>
<td align="center" valign="top">0.446<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.335<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.359<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.290<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">1</td>
<td/>
<td/>
</tr>
<tr>
<td align="left" valign="top">LE</td>
<td align="center" valign="top">1</td>
<td align="center" valign="top">7</td>
<td align="center" valign="top">4.466</td>
<td align="center" valign="top">1.351</td>
<td align="center" valign="top">0.427<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.296<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.350<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.235<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.561<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">1</td>
<td/>
</tr>
<tr>
<td align="left" valign="top">SEE</td>
<td align="center" valign="top">1</td>
<td align="center" valign="top">4</td>
<td align="center" valign="top">3.448</td>
<td align="center" valign="top">0.656</td>
<td align="center" valign="top">0.204<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.148<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.143<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.113<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.310<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.341<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">1</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<p>EL, emotional leisure; TR, teaching rules; AS, academic support; LC, life care; PEI, parental education involvement; PGI, personal growth initiative; LE, learning engagement; SEE, self-education expectation.</p>
<p>&#x002A;&#x002A;<italic>p</italic>&#x202F;&#x003C;&#x202F;0.01.</p>
</table-wrap-foot>
</table-wrap>
<table-wrap position="float" id="tab2">
<label>Table 2</label>
<caption>
<p>Descriptive statistics and bivariate correlations (grandparent).</p>
</caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th>Variable</th>
<th align="char" valign="top" char="&#x00D7;">
<italic>Min</italic>
</th>
<th align="char" valign="top" char="&#x00D7;">
<italic>Max</italic>
</th>
<th align="char" valign="top" char="&#x00D7;">
<italic>M</italic>
</th>
<th align="char" valign="top" char="&#x00D7;">
<italic>SD</italic>
</th>
<th align="char" valign="top" char="&#x00D7;">EL</th>
<th align="char" valign="top" char="&#x00D7;">TR</th>
<th align="char" valign="top" char="&#x00D7;">AS</th>
<th align="char" valign="top" char="&#x00D7;">LC</th>
<th align="char" valign="top" char="&#x00D7;">PGI</th>
<th align="char" valign="top" char="&#x00D7;">LE</th>
<th align="char" valign="top" char="&#x00D7;">SEE</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" valign="top">EL</td>
<td align="center" valign="top">1</td>
<td align="center" valign="top">5</td>
<td align="center" valign="top">2.842</td>
<td align="center" valign="top">0.816</td>
<td align="center" valign="top">1</td>
<td/>
<td/>
<td/>
<td/>
<td/>
<td/>
</tr>
<tr>
<td align="left" valign="top">TR</td>
<td align="center" valign="top">1</td>
<td align="center" valign="top">5</td>
<td align="center" valign="top">4.032</td>
<td align="center" valign="top">0.889</td>
<td align="center" valign="top">0.452<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">1</td>
<td/>
<td/>
<td/>
<td/>
<td/>
</tr>
<tr>
<td align="left" valign="top">AS</td>
<td align="center" valign="top">1</td>
<td align="center" valign="top">5</td>
<td align="center" valign="top">3.335</td>
<td align="center" valign="top">0.967</td>
<td align="center" valign="top">0.619<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.596<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">1</td>
<td/>
<td/>
<td/>
<td/>
</tr>
<tr>
<td align="left" valign="top">LC</td>
<td align="center" valign="top">1</td>
<td align="center" valign="top">5</td>
<td align="center" valign="top">4.005</td>
<td align="center" valign="top">0.847</td>
<td align="center" valign="top">0.438<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.462<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.501<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">1</td>
<td/>
<td/>
<td/>
</tr>
<tr>
<td align="left" valign="top">PGI</td>
<td align="center" valign="top">1</td>
<td align="center" valign="top">5</td>
<td align="center" valign="top">3.280</td>
<td align="center" valign="top">0.767</td>
<td align="center" valign="top">0.507<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.376<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.454<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.442<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">1</td>
<td/>
<td/>
</tr>
<tr>
<td align="left" valign="top">LE</td>
<td align="center" valign="top">1</td>
<td align="center" valign="top">7</td>
<td align="center" valign="top">4.495</td>
<td align="center" valign="top">1.257</td>
<td align="center" valign="top">0.384<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.336<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.460<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.384<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.629<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">1</td>
<td/>
</tr>
<tr>
<td align="left" valign="top">SEE</td>
<td align="center" valign="top">1</td>
<td align="center" valign="top">4</td>
<td align="center" valign="top">3.527</td>
<td align="center" valign="top">0.617</td>
<td align="center" valign="top">0.206<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.146<sup>&#x002A;</sup></td>
<td align="center" valign="top">0.233<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.189<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.246<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.320<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">1</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<p>EL, emotional leisure; TR, teaching rules; AS, academic support; LC, life care; PEI, parental education involvement; GEI, grandparental education involvement; PGI Personal growth initiative; LE Learning engagement; SEE, self-education expectation.</p>
<p>&#x002A;<italic>p</italic>&#x202F;&#x003C;&#x202F;0.05, &#x002A;&#x002A;<italic>p</italic>&#x202F;&#x003C;&#x202F;0.01.</p>
</table-wrap-foot>
</table-wrap>
</sec>
<sec id="sec16">
<label>3.2</label>
<title>Multiple regression analyses</title>
<p>Separate multiple regression analyses were conducted using the four dimensions of PEI and GEI as independent variables. As shown in <xref ref-type="table" rid="tab3">Tables 3</xref>, <xref ref-type="table" rid="tab4">4</xref>, we found that, after controlling for grade and prior academic achievement, the PEI results indicated that emotional leisure (<italic>&#x03B2;</italic> =&#x202F;0.333, <italic>p</italic> &#x003C;&#x202F;0.001) had the most decisive influence, whereas the GEI results showed that academic support (<italic>&#x03B2;</italic> =&#x202F;0.277, <italic>p</italic> &#x003C;&#x202F;0.01) was most influential.</p>
<table-wrap position="float" id="tab3">
<label>Table 3</label>
<caption>
<p>The results of multiple regression analyses (parent).</p>
</caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="left" valign="top" colspan="3">Model</th>
<th align="center" valign="top">
<italic>B</italic>
</th>
<th align="center" valign="top">
<italic>SE</italic>
</th>
<th align="center" valign="top">
<italic>&#x03B2;</italic>
</th>
<th align="center" valign="top">
<italic>t</italic>
</th>
<th align="center" valign="top">
<italic>p</italic>
</th>
<th align="center" valign="top">VIF</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" valign="top" colspan="3">Constant</td>
<td align="center" valign="top">1.184</td>
<td align="center" valign="top">0.325</td>
<td/>
<td align="center" valign="top">3.646</td>
<td align="center" valign="top">0.000</td>
<td/>
</tr>
<tr>
<td align="left" valign="top" colspan="2" rowspan="4">Independent variable</td>
<td align="left" valign="top">Emotional leisure</td>
<td align="center" valign="top">0.504</td>
<td align="center" valign="top">0.080</td>
<td align="center" valign="top">0.333</td>
<td align="center" valign="top">6.323</td>
<td align="center" valign="top">0.000</td>
<td align="center" valign="top">2.452</td>
</tr>
<tr>
<td align="left" valign="top">Teaching rules</td>
<td align="center" valign="top">0.033</td>
<td align="center" valign="top">0.078</td>
<td align="center" valign="top">0.020</td>
<td align="center" valign="top">0.422</td>
<td align="center" valign="top">0.673</td>
<td align="center" valign="top">1.911</td>
</tr>
<tr>
<td align="left" valign="top">Academic support</td>
<td align="center" valign="top">0.095</td>
<td align="center" valign="top">0.076</td>
<td align="center" valign="top">0.066</td>
<td align="center" valign="top">1.253</td>
<td align="center" valign="top">0.211</td>
<td align="center" valign="top">2.479</td>
</tr>
<tr>
<td align="left" valign="top">Life care</td>
<td align="center" valign="top">&#x2212;0.001</td>
<td align="center" valign="top">0.073</td>
<td align="center" valign="top">&#x2212;0.001</td>
<td align="center" valign="top">&#x2212;0.020</td>
<td align="center" valign="top">0.984</td>
<td align="center" valign="top">1.727</td>
</tr>
<tr>
<td align="left" valign="top" rowspan="7">Control variable</td>
<td align="left" valign="top" rowspan="2">Grade</td>
<td align="left" valign="top">Grade1</td>
<td align="center" valign="top">0.431</td>
<td align="center" valign="top">0.097</td>
<td align="center" valign="top">0.154</td>
<td align="center" valign="top">4.437</td>
<td align="center" valign="top">0.000</td>
<td align="center" valign="top">1.069</td>
</tr>
<tr>
<td align="left" valign="top">Grade2</td>
<td align="center" valign="top">0</td>
<td/>
<td/>
<td/>
<td/>
<td/>
</tr>
<tr>
<td align="left" valign="top" rowspan="5">Score ranking</td>
<td align="left" valign="top">Top</td>
<td align="center" valign="top">1.417</td>
<td align="center" valign="top">0.246</td>
<td align="center" valign="top">0.344</td>
<td align="center" valign="top">5.760</td>
<td align="center" valign="top">0.000</td>
<td align="center" valign="top">3.163</td>
</tr>
<tr>
<td align="left" valign="top">Above the average</td>
<td align="center" valign="top">1.301</td>
<td align="center" valign="top">0.221</td>
<td align="center" valign="top">0.436</td>
<td align="center" valign="top">5.884</td>
<td align="center" valign="top">0.000</td>
<td align="center" valign="top">4.862</td>
</tr>
<tr>
<td align="left" valign="top">Average</td>
<td align="center" valign="top">1.093</td>
<td align="center" valign="top">0.218</td>
<td align="center" valign="top">0.385</td>
<td align="center" valign="top">5.016</td>
<td align="center" valign="top">0.000</td>
<td align="center" valign="top">5.211</td>
</tr>
<tr>
<td align="left" valign="top">Below the average</td>
<td align="center" valign="top">0.595</td>
<td align="center" valign="top">0.228</td>
<td align="center" valign="top">0.173</td>
<td align="center" valign="top">2.609</td>
<td align="center" valign="top">0.009</td>
<td align="center" valign="top">3.911</td>
</tr>
<tr>
<td align="left" valign="top">Bottom</td>
<td align="center" valign="top">0</td>
<td/>
<td/>
<td/>
<td/>
<td/>
</tr>
<tr>
<td align="left" valign="top" colspan="5"><italic>R<sup>2</sup></italic></td>
<td align="center" valign="top" colspan="4">0.294</td>
</tr>
<tr>
<td align="left" valign="top" colspan="5"><italic>F</italic></td>
<td align="center" valign="top" colspan="4">28.869</td>
</tr>
<tr>
<td align="left" valign="top" colspan="5"><italic>p</italic></td>
<td align="center" valign="top" colspan="4">0.000</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap position="float" id="tab4">
<label>Table 4</label>
<caption>
<p>The results of multiple regression analyses (grandparent).</p>
</caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="left" valign="top" colspan="3">Model</th>
<th align="center" valign="top">
<italic>B</italic>
</th>
<th align="center" valign="top">
<italic>SE</italic>
</th>
<th align="center" valign="top">
<italic>&#x03B2;</italic>
</th>
<th align="center" valign="top">
<italic>t</italic>
</th>
<th align="center" valign="top">
<italic>p</italic>
</th>
<th align="center" valign="top">VIF</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" valign="top" colspan="3">Constant</td>
<td align="center" valign="top">0.892</td>
<td align="center" valign="top">0.702</td>
<td/>
<td align="center" valign="top">1.270</td>
<td align="center" valign="top">0.206</td>
<td/>
</tr>
<tr>
<td align="left" valign="top" colspan="2" rowspan="4">Independent variable</td>
<td align="left" valign="top">Emotional leisure</td>
<td align="center" valign="top">0.100</td>
<td align="center" valign="top">0.121</td>
<td align="center" valign="top">0.065</td>
<td align="center" valign="top">0.823</td>
<td align="center" valign="top">0.412</td>
<td align="center" valign="top">1.738</td>
</tr>
<tr>
<td align="left" valign="top">Teaching rules</td>
<td align="center" valign="top">0.055</td>
<td align="center" valign="top">0.109</td>
<td align="center" valign="top">0.039</td>
<td align="center" valign="top">0.499</td>
<td align="center" valign="top">0.619</td>
<td align="center" valign="top">1.682</td>
</tr>
<tr>
<td align="left" valign="top">Academic support</td>
<td align="center" valign="top">0.361</td>
<td align="center" valign="top">0.115</td>
<td align="center" valign="top">0.277</td>
<td align="center" valign="top">3.137</td>
<td align="center" valign="top">0.002</td>
<td align="center" valign="top">2.196</td>
</tr>
<tr>
<td align="left" valign="top">Life care</td>
<td align="center" valign="top">0.266</td>
<td align="center" valign="top">0.108</td>
<td align="center" valign="top">0.179</td>
<td align="center" valign="top">2.472</td>
<td align="center" valign="top">0.014</td>
<td align="center" valign="top">1.480</td>
</tr>
<tr>
<td align="left" valign="top" rowspan="7">Control variable</td>
<td align="left" valign="top" rowspan="2">Grade</td>
<td align="left" valign="top">Grade1</td>
<td align="center" valign="top">&#x2212;0.023</td>
<td align="center" valign="top">0.475</td>
<td align="center" valign="top">&#x2212;0.003</td>
<td align="center" valign="top">&#x2212;0.048</td>
<td align="center" valign="top">0.962</td>
<td align="center" valign="top">1.053</td>
</tr>
<tr>
<td align="left" valign="top">Grade2</td>
<td align="center" valign="top">0</td>
<td/>
<td/>
<td/>
<td/>
<td/>
</tr>
<tr>
<td align="left" valign="top" rowspan="5">Score ranking</td>
<td align="left" valign="top">Top</td>
<td align="center" valign="top">1.373</td>
<td align="center" valign="top">0.391</td>
<td align="center" valign="top">0.332</td>
<td align="center" valign="top">3.514</td>
<td align="center" valign="top">0.001</td>
<td align="center" valign="top">2.501</td>
</tr>
<tr>
<td align="left" valign="top">Above the average</td>
<td align="center" valign="top">1.259</td>
<td align="center" valign="top">0.325</td>
<td align="center" valign="top">0.479</td>
<td align="center" valign="top">3.875</td>
<td align="center" valign="top">0.000</td>
<td align="center" valign="top">4.286</td>
</tr>
<tr>
<td align="left" valign="top">Average</td>
<td align="center" valign="top">0.734</td>
<td align="center" valign="top">0.332</td>
<td align="center" valign="top">0.264</td>
<td align="center" valign="top">2.214</td>
<td align="center" valign="top">0.028</td>
<td align="center" valign="top">4.006</td>
</tr>
<tr>
<td align="left" valign="top">Below the average</td>
<td align="center" valign="top">0.319</td>
<td align="center" valign="top">0.346</td>
<td align="center" valign="top">0.101</td>
<td align="center" valign="top">0.922</td>
<td align="center" valign="top">0.358</td>
<td align="center" valign="top">3.404</td>
</tr>
<tr>
<td align="left" valign="top">Bottom</td>
<td align="center" valign="top">0</td>
<td/>
<td/>
<td/>
<td/>
<td/>
</tr>
<tr>
<td align="left" valign="top" colspan="5"><italic>R<sup>2</sup></italic></td>
<td align="center" valign="top" colspan="4">0.373</td>
</tr>
<tr>
<td align="left" valign="top" colspan="5"><italic>F</italic></td>
<td align="center" valign="top" colspan="4">11.647</td>
</tr>
<tr>
<td align="left" valign="top" colspan="5"><italic>p</italic></td>
<td align="center" valign="top" colspan="4">0.000</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
<sec id="sec17">
<label>3.3</label>
<title>Testing the mediation model</title>
<p>We employed Model 4 of PROCESS to examine the mediating effect of PGI between PEI/GEI and learning engagement. Percentile bootstrapping and bias-corrected percentile bootstrapping with 5,000 resamples were employed to construct 95% confidence intervals for the indirect effects. The four dimensions of parental/grandparental educational involvement represent different aspects of educational involvement, and they showed different correlations with learning engagement. Therefore, we will explore the relationship between educational involvement and learning engagement by dimension. After controlling for grade and previous achievement, four dimensions of parental education involvement significantly and positively predicted learning engagement in the absence of the mediator. Among them, the prediction power of emotional leisure is the strongest. Therefore, we mainly present the results of emotional leisure, as shown in <xref ref-type="table" rid="tab5">Table 5</xref>.</p>
<table-wrap position="float" id="tab5">
<label>Table 5</label>
<caption>
<p>Mediation effect of personal growth initiative in emotional leisure and learning engagement (parent).</p>
</caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="left" valign="top">Outcome variable</th>
<th align="left" valign="top">Predictor variable</th>
<th align="center" valign="top">
<italic>B</italic>
</th>
<th align="center" valign="top">
<italic>&#x03B2;</italic>
</th>
<th align="center" valign="top">
<italic>SE</italic>
</th>
<th align="center" valign="top">
<italic>t</italic>
</th>
<th align="center" valign="top">
<italic>p</italic>
</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" valign="bottom" rowspan="3">LE</td>
<td align="left" valign="bottom">Grade</td>
<td align="center" valign="top">0.421</td>
<td align="center" valign="bottom">&#x2212;0.152<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="bottom">0.095</td>
<td align="center" valign="bottom">&#x2212;4.420</td>
<td align="center" valign="top">0.000</td>
</tr>
<tr>
<td align="left" valign="bottom">Achievement</td>
<td align="center" valign="top">0.320</td>
<td align="center" valign="bottom">0.250<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="bottom">0.044</td>
<td align="center" valign="bottom">7.188</td>
<td align="center" valign="top">0.000</td>
</tr>
<tr>
<td align="left" valign="bottom">EL</td>
<td align="center" valign="top">0.591</td>
<td align="center" valign="bottom">0.391<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="bottom">0.052</td>
<td align="center" valign="bottom">11.425</td>
<td align="center" valign="top">0.000</td>
</tr>
<tr>
<td align="left" valign="bottom" rowspan="3">PGI</td>
<td align="left" valign="bottom">Grade</td>
<td align="center" valign="top">&#x2212;0.009</td>
<td align="center" valign="bottom">&#x2212;0.006</td>
<td align="center" valign="bottom">0.060</td>
<td align="center" valign="bottom">&#x2212;0.154</td>
<td align="center" valign="top">0.878</td>
</tr>
<tr>
<td align="left" valign="bottom">Achievement</td>
<td align="center" valign="top">0.116</td>
<td align="center" valign="bottom">0.151<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="bottom">0.028</td>
<td align="center" valign="bottom">4.154</td>
<td align="center" valign="top">0.000</td>
</tr>
<tr>
<td align="left" valign="bottom">EL</td>
<td align="center" valign="top">0.384</td>
<td align="center" valign="bottom">0.422<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="bottom">0.032</td>
<td align="center" valign="bottom">11.854</td>
<td align="center" valign="top">0.000</td>
</tr>
<tr>
<td align="left" valign="bottom" rowspan="4">LE</td>
<td align="left" valign="bottom">Grade</td>
<td align="center" valign="top">&#x2212;0.415</td>
<td align="center" valign="bottom">&#x2212;0.150<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="bottom">0.086</td>
<td align="center" valign="bottom">&#x2212;4.839</td>
<td align="center" valign="top">0.000</td>
</tr>
<tr>
<td align="left" valign="bottom">Achievement</td>
<td align="center" valign="top">0.239</td>
<td align="center" valign="bottom">0.187<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="bottom">0.041</td>
<td align="center" valign="bottom">5.887</td>
<td align="center" valign="top">0.000</td>
</tr>
<tr>
<td align="left" valign="bottom">EL</td>
<td align="center" valign="top">0.322</td>
<td align="center" valign="bottom">0.213<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="bottom">0.051</td>
<td align="center" valign="bottom">6.263</td>
<td align="center" valign="top">0.000</td>
</tr>
<tr>
<td align="left" valign="bottom">PGI</td>
<td align="center" valign="top">0.701</td>
<td align="center" valign="bottom">0.421<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="bottom">0.057</td>
<td align="center" valign="bottom">12.252</td>
<td align="center" valign="top">0.000</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<p>LE, learning engagement; PGI, personal growth initiative; EL, emotional leisure.</p>
<p>&#x002A;&#x002A;&#x002A;<italic>p</italic>&#x202F;&#x003C;&#x202F;0.01.</p>
</table-wrap-foot>
</table-wrap>
<p>As observed in <xref ref-type="table" rid="tab5">Tables 5</xref>, EL was positively correlated with PGI (<italic>&#x03B2;</italic>&#x202F;=&#x202F;0.422, <italic>p</italic>&#x202F;&#x003C;&#x202F;0.001). When EL was controlled for, PGI was positively correlated with learning engagement (<italic>&#x03B2;</italic>&#x202F;=&#x202F;0.421, <italic>p</italic>&#x202F;&#x003C;&#x202F;0.001). Moreover, when PGI was included, the association between EL and learning engagement remained significant (<italic>&#x03B2;</italic>&#x202F;=&#x202F;0.213, <italic>p</italic>&#x202F;&#x003C;&#x202F;0.001). Finally, a bias-corrected percentile bootstrap method was used to test the mediation model. We generated 5,000 bootstrapping samples from the original data (<italic>n</italic>&#x202F;=&#x202F;636 from parent data) by random sampling. The results (<xref ref-type="table" rid="tab6">Table 6</xref>) indicate that the indirect effect of PGI was 0.269, and its 95% CI was [0.192, 0.350] in the parent data. This mediating effect accounted for 45.516% of the total effect of the association between ER and learning engagement. In other words, PGI partially mediated the association between EL and learning engagement.</p>
<table-wrap position="float" id="tab6">
<label>Table 6</label>
<caption>
<p>Bootstrap test for mediating effect (parent).</p>
</caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="left" valign="top">Model pathways</th>
<th/>
<th align="center" valign="top">Effect</th>
<th align="center" valign="top">Boot LLCI</th>
<th align="center" valign="top">Boot ULCI</th>
<th align="center" valign="top">Ratio to total effect on LE</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" valign="middle">EL&#x202F;&#x2192;&#x202F;PGI&#x202F;&#x2192;&#x202F;LE</td>
<td align="left" valign="middle">Indirect effect</td>
<td align="center" valign="middle">0.269</td>
<td align="center" valign="middle">0.192</td>
<td align="center" valign="middle">0.350</td>
<td align="center" valign="middle">45.516%</td>
</tr>
<tr>
<td/>
<td align="left" valign="middle">Direct effect</td>
<td align="center" valign="middle">0.322</td>
<td align="center" valign="middle">0.221</td>
<td align="center" valign="middle">0.423</td>
<td/>
</tr>
<tr>
<td/>
<td align="left" valign="middle">Total effect</td>
<td align="center" valign="middle">0.591</td>
<td align="center" valign="middle">0.490</td>
<td align="center" valign="middle">0.693</td>
<td/>
</tr>
</tbody>
</table>
<table-wrap-foot>
<p>EL, emotional leisure; PGI, personal growth initiative; LE, learning engagement.</p>
</table-wrap-foot>
</table-wrap>
<p>Four dimensions of grandparental education involvement significantly and positively predicted learning engagement in the absence of the mediator, thus supporting H1. Among them, the prediction power of academic support (AS) is the strongest. Therefore, we mainly present the results of academic support, as shown in <xref ref-type="table" rid="tab7">Table 7</xref>.</p>
<table-wrap position="float" id="tab7">
<label>Table 7</label>
<caption>
<p>Mediation effect of PGI in academic support and learning engagement (grandparent).</p>
</caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="left" valign="top">Outcome variable</th>
<th align="left" valign="top">Predictor variable</th>
<th align="center" valign="top">
<italic>B</italic>
</th>
<th align="center" valign="top">
<italic>&#x03B2;</italic>
</th>
<th align="center" valign="top">
<italic>SE</italic>
</th>
<th align="center" valign="top">
<italic>t</italic>
</th>
<th align="center" valign="top">
<italic>p</italic>
</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" valign="bottom" rowspan="3">LE</td>
<td align="left" valign="bottom">Grade</td>
<td align="center" valign="top">&#x2212;0.052</td>
<td align="center" valign="bottom">&#x2212;0.007</td>
<td align="center" valign="bottom">0.470</td>
<td align="center" valign="bottom">&#x2212;0.110</td>
<td align="center" valign="top">0.912</td>
</tr>
<tr>
<td align="left" valign="bottom">Achievement</td>
<td align="center" valign="top">0.406</td>
<td align="center" valign="bottom">0.349<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="bottom">0.071</td>
<td align="center" valign="bottom">5.727</td>
<td align="center" valign="top">0.000</td>
</tr>
<tr>
<td align="left" valign="bottom">AS</td>
<td align="center" valign="top">0.552</td>
<td align="center" valign="bottom">0.424<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="bottom">0.079</td>
<td align="center" valign="bottom">6.966</td>
<td align="center" valign="top">0.000</td>
</tr>
<tr>
<td align="left" valign="bottom" rowspan="3">PGI</td>
<td align="left" valign="bottom">Grade</td>
<td align="center" valign="top">0.070</td>
<td align="center" valign="bottom">0.015</td>
<td align="center" valign="bottom">0.305</td>
<td align="center" valign="bottom">0.229</td>
<td align="center" valign="top">0.819</td>
</tr>
<tr>
<td align="left" valign="bottom">Achievement</td>
<td align="center" valign="top">0.143</td>
<td align="center" valign="bottom">0.202<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="bottom">0.046</td>
<td align="center" valign="bottom">3.112</td>
<td align="center" valign="top">0.002</td>
</tr>
<tr>
<td align="left" valign="bottom">AS</td>
<td align="center" valign="top">0.344</td>
<td align="center" valign="bottom">0.434<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="bottom">0.051</td>
<td align="center" valign="bottom">6.704</td>
<td align="center" valign="top">0.000</td>
</tr>
<tr>
<td align="left" valign="bottom" rowspan="4">LE</td>
<td align="left" valign="bottom">Grade</td>
<td align="center" valign="top">&#x2212;0.105</td>
<td align="center" valign="bottom">&#x2212;0.014</td>
<td align="center" valign="bottom">0.410</td>
<td align="center" valign="bottom">&#x2212;0.256</td>
<td align="center" valign="top">0.798</td>
</tr>
<tr>
<td align="left" valign="bottom">Achievement</td>
<td align="center" valign="top">0.297</td>
<td align="center" valign="bottom">0.255<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="bottom">0.063</td>
<td align="center" valign="bottom">4.682</td>
<td align="center" valign="top">0.000</td>
</tr>
<tr>
<td align="left" valign="bottom">AS</td>
<td align="center" valign="top">0.289</td>
<td align="center" valign="bottom">0.222<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="bottom">0.077</td>
<td align="center" valign="bottom">3.750</td>
<td align="center" valign="top">0.000</td>
</tr>
<tr>
<td align="left" valign="bottom">PGI</td>
<td align="center" valign="top">0.763</td>
<td align="center" valign="bottom">0.466<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="bottom">0.100</td>
<td align="center" valign="bottom">7.657</td>
<td align="center" valign="top">0.000</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<p>LE, learning engagement; PGI, personal growth initiative; AS, academic support.</p>
<p>&#x002A;&#x002A;<italic>p</italic>&#x202F;&#x003C;&#x202F;0.01, &#x002A;&#x002A;&#x002A;<italic>p</italic>&#x202F;&#x003C;&#x202F;0.001.</p>
</table-wrap-foot>
</table-wrap>
<p>As observed in <xref ref-type="table" rid="tab7">Table 7</xref>, AS was positively correlated with PGI (<italic>&#x03B2;</italic> =&#x202F;0.434, <italic>p</italic>&#x202F;&#x003C;&#x202F;0.001). When AS was controlled for, PGI was positively correlated with learning engagement (<italic>&#x03B2;</italic> =&#x202F;0.466, <italic>p</italic>&#x202F;&#x003C;&#x202F;0.001). Moreover, when PGI was included, the association between AS and learning engagement remained significant (<italic>&#x03B2;</italic> =&#x202F;0.222, <italic>p</italic>&#x202F;&#x003C;&#x202F;0.01). Finally, a bias-corrected percentile bootstrap method was used to test the mediation model. We generated 5,000 bootstrapping samples from the original data (<italic>n</italic>&#x202F;=&#x202F;186 from grandparent data) by random sampling. The results (<xref ref-type="table" rid="tab8">Table 8</xref>) indicate that the indirect effect of PGI was 0.263, and its 95% CI was [0.164, 0.364] in the parent data. This mediating effect accounted for 47.645% of the total effect of the association between AS and learning engagement. In other words, PGI partially mediated the association between AS and learning engagement. Thus, H2 was supported.</p>
<table-wrap position="float" id="tab8">
<label>Table 8</label>
<caption>
<p>Bootstrap test for mediating effect (grandparent).</p>
</caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="left" valign="top">Model pathways</th>
<th/>
<th align="center" valign="top">Effect</th>
<th align="center" valign="top">Boot LLCI</th>
<th align="center" valign="top">Boot ULCI</th>
<th align="center" valign="top">Ratio to total effect on LE</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" valign="middle">AS &#x2192; PGI&#x202F;&#x2192;&#x202F;LE</td>
<td align="left" valign="middle">Indirect effect</td>
<td align="center" valign="middle">0.263</td>
<td align="center" valign="middle">0.164</td>
<td align="center" valign="middle">0.364</td>
<td align="center" valign="middle">47.645%</td>
</tr>
<tr>
<td/>
<td align="left" valign="middle">Direct effect</td>
<td align="center" valign="middle">0.289</td>
<td align="center" valign="middle">0.137</td>
<td align="center" valign="middle">0.441</td>
<td/>
</tr>
<tr>
<td/>
<td align="left" valign="middle">Total effect</td>
<td align="center" valign="middle">0.552</td>
<td align="center" valign="middle">0.395</td>
<td align="center" valign="middle">0.708</td>
<td/>
</tr>
</tbody>
</table>
<table-wrap-foot>
<p>AS, academic support; PGI, personal growth initiative; LE, learning engagement.</p>
</table-wrap-foot>
</table-wrap>
</sec>
<sec id="sec18">
<label>3.4</label>
<title>Testing the moderated mediation model</title>
<p>We used Model 5 of PROCESS to determine whether the direct effect was moderated by self-education expectation. We introduced an interaction effect between self-education expectation and education involvement (emotional leisure, teaching rules, academic support, life care) to predict learning engagement. The unstandardized model estimates for H3a and H3b are presented in <xref ref-type="table" rid="tab9">Tables 9</xref>, <xref ref-type="table" rid="tab10">10</xref>, respectively. Due to space limitations, only the data results related to emotional leisure have been presented.</p>
<table-wrap position="float" id="tab9">
<label>Table 9</label>
<caption>
<p>Conditional process analysis in parent&#x2019;s data (emotional leisure).</p>
</caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th>Regression equation</th>
<th align="center" valign="top">
<italic>B</italic>
</th>
<th align="center" valign="top">
<italic>SE</italic>
</th>
<th align="center" valign="top">
<italic>t</italic>
</th>
<th align="center" valign="top">LLCI</th>
<th align="center" valign="top">ULCI</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" valign="top" colspan="6">Mediator variable model for predicting PGI</td>
</tr>
<tr>
<td align="left" valign="top">Constant</td>
<td align="center" valign="top">3.035</td>
<td align="center" valign="top">0.136</td>
<td align="center" valign="top">22.308<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">2.768</td>
<td align="center" valign="top">3.302</td>
</tr>
<tr>
<td align="left" valign="top">Grade</td>
<td align="center" valign="top">&#x2212;0.009</td>
<td align="center" valign="top">0.060</td>
<td align="center" valign="top">&#x2212;0.154</td>
<td align="center" valign="top">&#x2212;0.126</td>
<td align="center" valign="top">0.108</td>
</tr>
<tr>
<td align="left" valign="top">Achievement</td>
<td align="center" valign="top">0.116</td>
<td align="center" valign="top">0.028</td>
<td align="center" valign="top">4.154<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.061</td>
<td align="center" valign="top">0.170</td>
</tr>
<tr>
<td align="left" valign="top">EL</td>
<td align="center" valign="top">0.384</td>
<td align="center" valign="top">0.032</td>
<td align="center" valign="top">11.854<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.320</td>
<td align="center" valign="top">0.447</td>
</tr>
<tr>
<td align="left" valign="top" colspan="6">Dependent variable model for predicting LE</td>
</tr>
<tr>
<td align="left" valign="top">Constant</td>
<td align="center" valign="top">2.066</td>
<td align="center" valign="top">0.267</td>
<td align="center" valign="top">7.743<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">1.542</td>
<td align="center" valign="top">2.590</td>
</tr>
<tr>
<td align="left" valign="top">Grade</td>
<td align="center" valign="top">&#x2212;0.375</td>
<td align="center" valign="top">0.086</td>
<td align="center" valign="top">&#x2212;4.348<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">&#x2212;0.544</td>
<td align="center" valign="top">&#x2212;0.206</td>
</tr>
<tr>
<td align="left" valign="top">Achievement</td>
<td align="center" valign="top">0.208</td>
<td align="center" valign="top">0.042</td>
<td align="center" valign="top">4.916<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.125</td>
<td align="center" valign="top">0.291</td>
</tr>
<tr>
<td align="left" valign="top">EL</td>
<td align="center" valign="top">0.317</td>
<td align="center" valign="top">0.051</td>
<td align="center" valign="top">6.209<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.217</td>
<td align="center" valign="top">0.417</td>
</tr>
<tr>
<td align="left" valign="top">PGI</td>
<td align="center" valign="top">0.667</td>
<td align="center" valign="top">0.058</td>
<td align="center" valign="top">11.517<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.553</td>
<td align="center" valign="top">0.781</td>
</tr>
<tr>
<td align="left" valign="top">SEE</td>
<td align="center" valign="top">0.119</td>
<td align="center" valign="top">0.072</td>
<td align="center" valign="top">1.644</td>
<td align="center" valign="top">&#x2212;0.023</td>
<td align="center" valign="top">0.260</td>
</tr>
<tr>
<td align="left" valign="top">EL&#x202F;&#x00D7;&#x202F;SEE</td>
<td align="center" valign="top">&#x2212;0.214</td>
<td align="center" valign="top">0.069</td>
<td align="center" valign="top">&#x2212;3.112<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">&#x2212;0.349</td>
<td align="center" valign="top">&#x2212;0.079</td>
</tr>
</tbody>
</table>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="left" valign="top" colspan="6">Conditional direct effect analysis at values of the moderator</th>
</tr>
<tr>
<th align="left" valign="top">SEE</th>
<th align="center" valign="top">Effect</th>
<th align="center" valign="top">
<italic>SE</italic>
</th>
<th align="center" valign="top">
<italic>t</italic>
</th>
<th align="center" valign="top">LLCI</th>
<th align="center" valign="top">ULCI</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" valign="top">Low (M&#x202F;&#x2212;&#x202F;1SD)</td>
<td align="center" valign="top">0.457</td>
<td align="center" valign="top">0.069</td>
<td align="center" valign="top">6.661<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.323</td>
<td align="center" valign="top">0.592</td>
</tr>
<tr>
<td align="left" valign="top">Mean</td>
<td align="center" valign="top">0.317</td>
<td align="center" valign="top">0.051</td>
<td align="center" valign="top">6.209<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.217</td>
<td align="center" valign="top">0.417</td>
</tr>
<tr>
<td align="left" valign="top">High (M&#x202F;+&#x202F;1SD)</td>
<td align="center" valign="top">0.199</td>
<td align="center" valign="top">0.063</td>
<td align="center" valign="top">3.150<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.075</td>
<td align="center" valign="top">0.323</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<p>PGI, personal growth initiative; EL, emotional leisure; LE, learning engagement; SEE, self-education expectation.</p>
<p>&#x002A;&#x002A;<italic>p</italic>&#x202F;&#x003C;&#x202F;0.01, &#x002A;&#x002A;&#x002A;<italic>p</italic>&#x202F;&#x003C;&#x202F;0.001.</p>
</table-wrap-foot>
</table-wrap>
<table-wrap position="float" id="tab10">
<label>Table 10</label>
<caption>
<p>Conditional process analysis in grandparent&#x2019;s data (emotional leisure).</p>
</caption>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th>Regression equation</th>
<th align="center" valign="top">
<italic>B</italic>
</th>
<th align="center" valign="top">
<italic>SE</italic>
</th>
<th align="center" valign="top">
<italic>t</italic>
</th>
<th align="center" valign="top">LLCI</th>
<th align="center" valign="top">ULCI</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" valign="top" colspan="6">Mediator variable model for predicting PGI</td>
</tr>
<tr>
<td align="left" valign="top">Constant</td>
<td align="center" valign="top">2.720</td>
<td align="center" valign="top">0.333</td>
<td align="center" valign="top">8.177<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">2.064</td>
<td align="center" valign="top">3.377</td>
</tr>
<tr>
<td align="left" valign="top">Grade</td>
<td align="center" valign="top">0.169</td>
<td align="center" valign="top">0.298</td>
<td align="center" valign="top">0.567</td>
<td align="center" valign="top">&#x2212;0.418</td>
<td align="center" valign="top">0.756</td>
</tr>
<tr>
<td align="left" valign="top">Achievement</td>
<td align="center" valign="top">0.120</td>
<td align="center" valign="top">0.045</td>
<td align="center" valign="top">2.653<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.031</td>
<td align="center" valign="top">0.209</td>
</tr>
<tr>
<td align="left" valign="top">EL</td>
<td align="center" valign="top">0.454</td>
<td align="center" valign="top">0.060</td>
<td align="center" valign="top">7.594<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.336</td>
<td align="center" valign="top">0.572</td>
</tr>
<tr>
<td align="left" valign="top" colspan="6">Dependent variable model for predicting LE</td>
</tr>
<tr>
<td align="left" valign="top">Constant</td>
<td align="center" valign="top">1.019</td>
<td align="center" valign="top">0.537</td>
<td align="center" valign="top">1.899</td>
<td align="center" valign="top">&#x2212;0.040</td>
<td align="center" valign="top">2.078</td>
</tr>
<tr>
<td align="left" valign="top">Grade</td>
<td align="center" valign="top">&#x2212;0.133</td>
<td align="center" valign="top">0.409</td>
<td align="center" valign="top">&#x2212;0.325</td>
<td align="center" valign="top">&#x2212;0.939</td>
<td align="center" valign="top">0.673</td>
</tr>
<tr>
<td align="left" valign="top">Achievement</td>
<td align="center" valign="top">0.252</td>
<td align="center" valign="top">0.064</td>
<td align="center" valign="top">3.931<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.125</td>
<td align="center" valign="top">0.378</td>
</tr>
<tr>
<td align="left" valign="top">EL</td>
<td align="center" valign="top">0.102</td>
<td align="center" valign="top">0.094</td>
<td align="center" valign="top">1.078</td>
<td align="center" valign="top">&#x2212;0.084</td>
<td align="center" valign="top">0.288</td>
</tr>
<tr>
<td align="left" valign="top">PGI</td>
<td align="center" valign="top">0.869</td>
<td align="center" valign="top">0.103</td>
<td align="center" valign="top">8.446<sup>&#x002A;&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.666</td>
<td align="center" valign="top">1.071</td>
</tr>
<tr>
<td align="left" valign="top">SEE</td>
<td align="center" valign="top">0.172</td>
<td align="center" valign="top">0.115</td>
<td align="center" valign="top">1.494</td>
<td align="center" valign="top">&#x2212;0.055</td>
<td align="center" valign="top">0.400</td>
</tr>
<tr>
<td align="left" valign="top">EL&#x202F;&#x00D7;&#x202F;SEE</td>
<td align="center" valign="top">&#x2212;0.480</td>
<td align="center" valign="top">0.136</td>
<td align="center" valign="top">&#x2212;3.533<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">&#x2212;0.748</td>
<td align="center" valign="top">&#x2212;0.212</td>
</tr>
</tbody>
</table>
<table frame="hsides" rules="groups">
<thead>
<tr>
<th align="left" valign="top" colspan="6">Conditional direct effect analysis at values of the moderator</th>
</tr>
<tr>
<th align="left" valign="top">SEE</th>
<th align="center" valign="top">Effect</th>
<th align="center" valign="top">
<italic>SE</italic>
</th>
<th align="center" valign="top">
<italic>t</italic>
</th>
<th align="center" valign="top">LLCI</th>
<th align="center" valign="top">ULCI</th>
</tr>
</thead>
<tbody>
<tr>
<td align="left" valign="top">Low (M&#x202F;&#x2212;&#x202F;1SD)</td>
<td align="center" valign="top">0.398</td>
<td align="center" valign="top">0.127</td>
<td align="center" valign="top">3.125<sup>&#x002A;&#x002A;</sup></td>
<td align="center" valign="top">0.220</td>
<td align="center" valign="top">0.796</td>
</tr>
<tr>
<td align="left" valign="top">Mean</td>
<td align="center" valign="top">0.102</td>
<td align="center" valign="top">0.094</td>
<td align="center" valign="top">1.078</td>
<td align="center" valign="top">0.045</td>
<td align="center" valign="top">0.502</td>
</tr>
<tr>
<td align="left" valign="top">High (M&#x202F;+&#x202F;1SD)</td>
<td align="center" valign="top">&#x2212;0.125</td>
<td align="center" valign="top">0.113</td>
<td align="center" valign="top">&#x2212;1.107</td>
<td align="center" valign="top">&#x2212;0.349</td>
<td align="center" valign="top">0.098</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<p>PGI, personal growth initiative; EL, emotional leisure; LE, learning engagement; SEE, self-education expectation.</p>
<p>&#x002A;<italic>p</italic>&#x202F;&#x003C;&#x202F;0.05, &#x002A;&#x002A;<italic>p</italic>&#x202F;&#x003C;&#x202F;0.01, &#x002A;&#x002A;&#x002A;<italic>p</italic>&#x202F;&#x003C;&#x202F;0.001.</p>
</table-wrap-foot>
</table-wrap>
<p>For the situation where parents directly raise their children, the interaction term (emotional leisure/teaching rules/academic support &#x00D7; self-education expectation) significantly predicted learning engagement, indicating that self-education expectation moderated the direct effect of emotional leisure, teaching rules, academic support on learning engagement, thereby supporting H3a partially. The positive direct effect of emotional leisure, academic support on learning engagement was significant for individuals with low and high self-education expectation. However, the same positive direct effect of teaching rules was significant only for individuals with low self-education expectation. To better understand the moderating effect of self-education expectation, plots of the relationship between emotional leisure, academic support, teaching rules and learning engagement, at two levels of self-education expectation (1 SD below the mean and 1 SD above the mean) are depicted in <xref ref-type="fig" rid="fig2">Figures 2</xref>&#x2013;<xref ref-type="fig" rid="fig4">4</xref>, respectively.</p>
<fig position="float" id="fig2">
<label>Figure 2</label>
<caption>
<p>Interaction effect of self-education expectation and emotional leisure on learning engagement.</p>
</caption>
<graphic xlink:href="fpsyg-16-1564880-g002.tif" mimetype="image" mime-subtype="tiff">
<alt-text content-type="machine-generated">Line graph showing learning engagement on the y-axis and emotional leisure on the x-axis, with categories Low (M-1SD) and High (M+1SD). Two lines, one solid representing "High" and one dashed representing "Low," indicate learning engagement increases with higher emotional leisure.</alt-text>
</graphic>
</fig>
<fig position="float" id="fig3">
<label>Figure 3</label>
<caption>
<p>Interaction effect of self-education expectation and academic support on learning engagement.</p>
</caption>
<graphic xlink:href="fpsyg-16-1564880-g003.tif" mimetype="image" mime-subtype="tiff">
<alt-text content-type="machine-generated">Two lines, Low (M-1SD) and High (M+1SD), indicate increased learning engagement with higher academic support. Lowgroup shows a sharper increase.</alt-text>
</graphic>
</fig>
<fig position="float" id="fig4">
<label>Figure 4</label>
<caption>
<p>Interaction effect of self-education expectation and teaching rules on learning engagement.</p>
</caption>
<graphic xlink:href="fpsyg-16-1564880-g004.tif" mimetype="image" mime-subtype="tiff">
<alt-text content-type="machine-generated">Line graph showing the relationship between teaching rules and learning engagement, with engagement on the y-axis and rules on the x-axis. Two lines depict different levels of self-education expectation: a dashed line for low (M-1SD) and a solid line for high (M+1SD). Both lines show an upward trend as teaching rules increase.</alt-text>
</graphic>
</fig>
<p>For the situation where grandparents providing caregiving for grandchildren, only the interaction term emotional leisure &#x00D7; self-education expectation significantly predicted learning engagement, indicating that self-education expectation moderated the direct effect of emotional leisure on learning engagement, thereby supporting H3a partially. Meanwhile, the positive direct effect of emotional leisure was significant only for individuals with low self-education expectation. To better understand the moderating effect of self-education expectation, plot of the relationship between emotional leisure and learning engagement, at two levels of self-education expectation (1 SD below the mean and 1 SD above the mean) is depicted in <xref ref-type="fig" rid="fig5">Figure 5</xref>.</p>
<fig position="float" id="fig5">
<label>Figure 5</label>
<caption>
<p>Interaction effect of self-education expectation and grandparental education involvement on learning engagement.</p>
</caption>
<graphic xlink:href="fpsyg-16-1564880-g005.tif" mimetype="image" mime-subtype="tiff">
<alt-text content-type="machine-generated">Line graph showing learning engagement versus emotional leisure, with self-education expectation as the variable. Two lines represent Low (M-1SD) and High (M+1SD) self-education expectation. Low expectation shows a positive trend, while high expectation the direct effect between emotional leisure and learning engagement was not significant (grandparents&#x2019; data).</alt-text>
</graphic>
</fig>
<p>As observed in <xref ref-type="table" rid="tab10">Table 10</xref> and <xref ref-type="fig" rid="fig5">Figure 5</xref>, for individuals with low self-education expectation, emotional leisure was positively associated with learning engagement (conditional effect&#x202F;=&#x202F;0.398, <italic>SE</italic> =&#x202F;0.127, 95% CI&#x202F;=&#x202F;[0.220, 0.796]). For individuals with high self-education expectation, the direct effect between emotional leisure and learning engagement was not significant (95% CI&#x202F;=&#x202F;[&#x2212;0.349, 0.098]).</p>
</sec>
</sec>
<sec sec-type="discussion" id="sec19">
<label>4</label>
<title>Discussion</title>
<p>This study explored the relationships between PEI/GEI and adolescents&#x2019; learning engagement in the Chinese cultural context, as well as the mechanisms underlying these relationships. The results indicated that PEI and GEI not only directly influenced learning engagement, but also exhibited an indirect effect mediated by PGI. For parental education involvement, among the four dimensions of emotional leisure, teaching rules, academic support, and life care, the correlation between emotional leisure and learning engagement is the greatest. For grandparental education involvement, among the four dimensions of emotional leisure, teaching rules, academic support, and life care, the correlation between academic support and learning engagement is the greatest. The interaction effect between self-education expectation and education involvement (emotional leisure, teaching rules, academic support, life care) to predict learning engagement are different between parent and grandparent. The findings contribute to a better understanding of how and when PEI and GEI are associated with learning engagement.</p>
<sec id="sec20">
<label>4.1</label>
<title>PEI/GEI and learning engagement</title>
<p>We observed that both PEI and GEI positively predicted adolescents&#x2019; learning engagement, which aligns with existing theoretical perspectives and empirical evidence. Positive parenting styles can directly influence adolescents&#x2019; psychological development (<xref ref-type="bibr" rid="ref6">Bi et al., 2024</xref>). A positive association between PEI/GEI and heightened learning engagement levels ultimately predicts elevated academic achievement (<xref ref-type="bibr" rid="ref11">Day and Dotterer, 2018</xref>; <xref ref-type="bibr" rid="ref21">Hoover-Dempsey and Sandler, 1995</xref>; <xref ref-type="bibr" rid="ref46">Skinner et al., 2009</xref>). This implies that individuals who experience greater PEI/GEI are more inclined to engage in learning activities. Drawing on social capital theory, family, as a significant social network, expands students&#x2019; social capital, providing more learning opportunities and resources. Meanwhile, four dimensions of parental education involvement significantly and positively predicted learning engagement in the absence of the mediator. In parents&#x2019; data, the prediction power of emotional leisure is the strongest. Compared with grandparents, parents are stricter with their children. Therefore, children need more leisure activities when they are with their parents. Positive emotional experiences from nature are of significance (<xref ref-type="bibr" rid="ref48">Wang et al., 2025</xref>). Leisure activities positively predicted positive emotion (<xref ref-type="bibr" rid="ref54">Zhang and Zheng, 2017</xref>) which helpful for learning engagement. In grandparents&#x2019; data, the prediction power of academic support is the strongest. Grandparents can, to a certain extent, make up for the lack of educational support caused by the absence of parents by means such as supervising homework and helping solve learning difficulties, thus enabling children to devote themselves to their studies.</p>
</sec>
<sec id="sec21">
<label>4.2</label>
<title>Mediating role of PGI</title>
<p>Our study not only revealed that PEI, GEI, and PGI positively predict learning engagement, but also unveiled the mediating role of PGI in the relationships between PEI/GEI and learning engagement. This finding aligns with previous studies supporting the idea that students who experience PEI/GEI are more likely to value their learning, thus promoting autonomous motivation (<xref ref-type="bibr" rid="ref40">Schmid and Garrels, 2021</xref>). According to Deci and Ryan&#x2019;s self-determination theory (<xref ref-type="bibr" rid="ref47">Vansteenkiste et al., 2020</xref>), individuals have three basic psychological needs: autonomy, relatedness, and competence. PEI and GEI play a crucial role in shaping children&#x2019;s future development, fostering autonomy, and motivating active participation in self-regulated learning (<xref ref-type="bibr" rid="ref1">Ahmed et al., 2024</xref>). When adolescents&#x2019; basic needs are satisfied, they are more motivated to engage in their growth process and have higher expectations for their future academic life (<xref ref-type="bibr" rid="ref24">Leversen et al., 2012</xref>). Parents and grandparents who are positively involved in offering academic assistance or life care satisfy students&#x2019; psychological needs and foster their autonomous motivation for learning. As a vital component of an individual&#x2019;s inner psychological resources, PGI plays a mediating role in the connections between PEI/GEI and adolescents&#x2019; learning engagement. A supportive family atmosphere fosters stronger autonomous motivation, and adolescents will have higher expectations for learning when they are effectively assisted in developing positive character traits such as PGI (<xref ref-type="bibr" rid="ref5">Benneker et al., 2023</xref>). Furthermore, adolescents who grow up in such environments often have more positive experiences, experience better psychological wellbeing, and exhibit greater life satisfaction (<xref ref-type="bibr" rid="ref50">Wang et al., 2018</xref>). Consequently, they are more likely to enjoy their academic lives, which in turn influences their learning engagement.</p>
</sec>
<sec id="sec22">
<label>4.3</label>
<title>Moderating effect of self-education expectation</title>
<p>Our study revealed that adolescents&#x2019; self-education expectation moderated the relationships between PEI/GEI and learning engagement. In the data of the parents, the interaction term (emotional leisure/teaching rules/academic support &#x00D7; self-education expectation) significantly predicted learning engagement, indicating that self-education expectation moderated the direct effect of emotional leisure, teaching rules, academic support on learning engagement. In the data of grandparents, only the interaction term emotional leisure &#x00D7; self-education expectation significantly predicted learning engagement, indicating that self-education expectation moderated the direct effect of emotional leisure on learning engagement.</p>
<p>Specifically, these relationships were stronger among adolescents with lower self-education expectations than among those with higher expectations. According to existing research, adolescents with higher academic achievement expectations are more likely to prioritize personal effort and autonomous motivation (<xref ref-type="bibr" rid="ref44">Shengyao et al., 2024</xref>). Conversely, when adolescents lack aspirations for improved academic achievement, PEI/GEI can instill a sense of responsibility and motivation, driven by the desire not to disappoint their parents/grandparents, thereby empowering them to tackle challenging learning tasks more effectively. In this context, PEI/GEI serves as a source of stability and reassurance, assisting adolescents in navigating diverse obstacles. Such experiences can enhance adolescents&#x2019; awareness of the support they receive from others, ultimately promoting their learning engagement (<xref ref-type="bibr" rid="ref28">Luo et al., 2020</xref>).</p>
<p>However, the moderating mechanisms of self-education expectation may differ depending on adolescents&#x2019; perceived PEI/GEI. In the data of the parents, for individuals with low self-education expectation and high self-education expectation, the positive direct effects of both emotional leisure and academic support on learning engagement were significant. However, the positive direct effect of teaching rules on learning engagement was not significant for individuals with high self-education expectation. This means that, for individuals with high self-education expectations, teaching rules did not affect learning engagement. In the data of the grandparents, self-education expectation only moderated the direct effect of emotional leisure on learning engagement. For individuals with low self-education expectation, emotional leisure was positively associated with learning engagement. For individuals with high self-education expectation, the direct effect between emotional leisure and learning engagement was not significant. In China, the ways and values of parents and grandparents differ significantly (<xref ref-type="bibr" rid="ref27">Lu et al., 2022</xref>). Parents were more influenced by modernization and urbanization, with a greater emphasis on academic performance, personal achievement, and social status. Thus, they may be more inclined to use modern educational resources and methods, such as cram schools and online education, in the hope that their children will stand out from the fierce competition (<xref ref-type="bibr" rid="ref9">Chen et al., 2021</xref>). According to existing research, children&#x2019;s learning engagement is positively related to both paternal and maternal involvement (<xref ref-type="bibr" rid="ref26">Li et al., 2023</xref>). However, grandparents tend to pay more attention to the inheritance of traditional values (<xref ref-type="bibr" rid="ref53">Zhang and Wu, 2021</xref>) or children&#x2019;s health outcomes (<xref ref-type="bibr" rid="ref34">Pulgaron et al., 2016</xref>). Thus, grandparents&#x2019; influence might differ owing to generational gaps and differing perspectives on education (<xref ref-type="bibr" rid="ref17">Grolnick and Pomerantz, 2022</xref>). While grandparents may still play a role, their influence may be indirect or less pronounced than that of parents (<xref ref-type="bibr" rid="ref15">Dunifon and Bajracharya, 2012</xref>).</p>
</sec>
<sec id="sec23">
<label>4.4</label>
<title>Research significance and limitations</title>
<p>This study has important theoretical and practical implications. First, it aligns with the theory of positive adolescent development, which emphasizes how adolescents&#x2019; external environments interact with their inner strengths to shape their learning engagement. This offers effective strategies for fostering adolescents&#x2019; learning behaviors. Second, there is an urgent need to prioritize the promotion of autonomous motivation and initiative among adolescents. This can be achieved by clarifying their learning goals and fostering personal growth dynamics. These qualities play a pivotal role in adolescents&#x2019; learning behaviors and growth processes, equipping them with resilience to overcome challenges and fulfill their potential.</p>
<p>Regarding practical implications, this study considers the discrepancy mechanisms in which PEI/GEI affects students&#x2019; learning engagement. The situation where parents raise their children themselves, along with taking them to educational places like science museums, engaging in leisure activities such as traveling or exercising, can help enhance children&#x2019;s learning engagement. When parents work in other places and the children are raised by their grandparents, the grandparents providing necessary academic support for the children can help increase their learning engagement. However, for the elderly with lower educational levels, this is very difficult to achieve. Meanwhile, the results of the moderation effect revealed that parents play a more important role in contributing to children&#x2019;s learning.</p>
<p>Despite the valuable insights provided by this study, it has some limitations. First, the study&#x2019;s scope was confined to one secondary school in China, potentially introducing regional bias and limiting the generalizability of the results. To enhance the reliability and applicability of our findings, future research should expand the sample size and consider diverse cultural contexts. Second, longitudinal studies and follow-up surveys could offer a more dynamic and holistic comprehension of PEI and adolescents&#x2019; learning engagement; thus, longitudinal studies should be conducted in the future.</p>
</sec>
</sec>
<sec sec-type="conclusions" id="sec24">
<label>5</label>
<title>Conclusion</title>
<p>Based on an analysis of the research data, a few conclusions were drawn in this study. PEI and GEI in middle-school students positively predict learning engagement. In a family environment that provides greater involvement and support, middle-school students tend to engage in more learning activities. In the context of parental education involvement, the most important factor in promoting learning engagement is emotional leisure. In the context of grandparental education involvement, the most important factor in promoting learning engagement is academic support. Meanwhile, individuals with a higher level of PGI are more willing to engage in learning. Additionally, in the context of parental education involvement, self-education expectation moderated the direct effect of emotional leisure, teaching rules, academic support on learning engagement. Meanwhile, the effect of emotional leisure, academic support on children&#x2019;s learning engagement was stronger among individuals with lower self-education expectation. The effect of teaching rules on children&#x2019;s learning engagement was significant only among individuals with low self-education expectation. In the context of grandparental education involvement, self-education expectation only moderated the direct effect of emotional leisure on learning engagement. Meanwhile, the effect of emotional leisure on children&#x2019;s learning engagement was significant only among individuals with low self-education expectation.</p>
</sec>
</body>
<back>
<sec sec-type="data-availability" id="sec25">
<title>Data availability statement</title>
<p>The raw data supporting the conclusions of this article will be made available by the authors without undue reservation.</p>
</sec>
<sec sec-type="ethics-statement" id="sec26">
<title>Ethics statement</title>
<p>The studies involving humans were approved by School of Psychology, Fujian Normal University. The studies were conducted in accordance with the local legislation and institutional requirements. Written informed consent for participation in this study was provided by the participants&#x2019; legal guardians/next of kin.</p>
</sec>
<sec sec-type="author-contributions" id="sec27">
<title>Author contributions</title>
<p>XX: Funding acquisition, Supervision, Writing &#x2013; review &#x0026; editing, Formal analysis. XH: Writing &#x2013; original draft, Methodology. MZ: Data curation, Writing &#x2013; original draft. JW: Writing &#x2013; original draft. QS: Writing &#x2013; review &#x0026; editing.</p>
</sec>
<sec sec-type="funding-information" id="sec28">
<title>Funding</title>
<p>The author(s) declare that financial support was received for the research and/or publication of this article. This research was supported by the Social Science Fund Project of Fujian Province of China (FJ2023B019).</p>
</sec>
<sec sec-type="COI-statement" id="sec29">
<title>Conflict of interest</title>
<p>The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec sec-type="ai-statement" id="sec30">
<title>Generative AI statement</title>
<p>The author(s) declare that no Gen AI was used in the creation of this manuscript.</p>
</sec>
<sec sec-type="disclaimer" id="sec31">
<title>Publisher&#x2019;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
<fn-group>
<fn id="fn0001"><p><sup>1</sup><ext-link xlink:href="http://www.afhayes.com" ext-link-type="uri">http://www.afhayes.com</ext-link></p></fn>
</fn-group>
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